Accurate characterization of coherent vortex structures in high-speed turbulent boundary layers presents a persistent challenge due to the flow’s high dimensionality and nonlinear dynamics. This study investigates an optimized decomposition framework that integrates modal decomposition techniques with a novel vortex identification strategy to extract dynamically significant features. The numerical solution from a previously conducted high-fidelity simulation of MVG-controlled supersonic flow serves as the testbed. Principal Component Decomposition and Non-negative Matrix Factorization are applied across multiple flow variables to evaluate their effectiveness in isolating coherent structures. The results show that, across the velocity-based cases, 3–4 modes capture 70% of the TKE with MSE about 0.1, while the Liutex case requires 14 modes but achieves a lower MSE of about 0.04. Overall, using the same number of modes yields similar reconstruction performance across all cases. The influence of various normalization and rescaling methods on decomposition performance is also examined. Optimization is guided by two primary criteria: the interpretability of spatial modes and MSE in reconstructing vortex structures. By employing low-rank matrix representations, this optimization study aims to enhance interpretability and reduce computational costs. This approach establishes a mathematically rigorous and efficient platform for analyzing vortex dynamics, achieving significant dimensionality reduction while preserving key features of turbulent transport.
Shaaban et al. (Mon,) studied this question.